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An electron strikes on a macroscopic target and recoils back. A closer look shows the electron to scatter backward after interacting with the proton.
A subatomic particle scatters straight backward from a target particle. In experiments seeking evidence for quarks, electrons were observed to occasionally scatter straight backward from a proton.

Section summary

  • The conservation of momentum principle is written
    p tot = constant size 12{p rSub { size 8{"tot"} } ="constant"} {}
    or
    p tot = p tot ( isolated system ) , size 12{p rSub { size 8{"tot"} } =p' rSub { size 8{"tot"} } ````` \( "isolated system" \) ,} {}
    p tot size 12{p rSub { size 8{"tot"} } } {} is the initial total momentum and p tot size 12{ ital "p'" rSub { size 8{"tot"} } } {} is the total momentum some time later.
  • An isolated system is defined to be one for which the net external force is zero F net = 0 . size 12{ left (F rSub { size 8{ ital "net"} } =0 right ) "." } {}
  • During projectile motion and where air resistance is negligible, momentum is conserved in the horizontal direction because horizontal forces are zero.
  • Conservation of momentum applies only when the net external force is zero.
  • The conservation of momentum principle is valid when considering systems of particles.

Conceptual questions

Professional Application

If you dive into water, you reach greater depths than if you do a belly flop. Explain this difference in depth using the concept of conservation of energy. Explain this difference in depth using what you have learned in this chapter.

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Under what circumstances is momentum conserved?

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Can momentum be conserved for a system if there are external forces acting on the system? If so, under what conditions? If not, why not?

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Momentum for a system can be conserved in one direction while not being conserved in another. What is the angle between the directions? Give an example.

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Professional Application

Explain in terms of momentum and Newton’s laws how a car’s air resistance is due in part to the fact that it pushes air in its direction of motion.

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Can objects in a system have momentum while the momentum of the system is zero? Explain your answer.

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Must the total energy of a system be conserved whenever its momentum is conserved? Explain why or why not.

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Problems&Exercises

Professional Application

Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 150,000 kg and a velocity of 0.300 m/s, and the second having a mass of 110,000 kg and a velocity of 0 . 120 m/s size 12{ - 0 "." "120"`"m/s"} {} . (The minus indicates direction of motion.) What is their final velocity?

0.122 m/s

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Suppose a clay model of a koala bear has a mass of 0.200 kg and slides on ice at a speed of 0.750 m/s. It runs into another clay model, which is initially motionless and has a mass of 0.350 kg. Both being soft clay, they naturally stick together. What is their final velocity?

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Professional Application

Consider the following question: A car moving at 10 m/s crashes into a tree and stops in 0.26 s. Calculate the force the seatbelt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70 kg. Would the answer to this question be different if the car with the 70-kg passenger had collided with a car that has a mass equal to and is traveling in the opposite direction and at the same speed? Explain your answer.

In acollision withan identicalcar, momentumis conserved.Afterwards v f = 0 for bothcars. Thechange inmomentum willbe thesame asin thecrash withthe tree.However, theforce onthe bodyis notdetermined sincethe timeis notknown. Apadded stopwill reduceinjurious forceon body.

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What is the velocity of a 900-kg car initially moving at 30.0 m/s, just after it hits a 150-kg deer initially running at 12.0 m/s in the same direction? Assume the deer remains on the car.

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A 1.80-kg falcon catches a 0.650-kg dove from behind in midair. What is their velocity after impact if the falcon’s velocity is initially 28.0 m/s and the dove’s velocity is 7.00 m/s in the same direction?

22.4 m/s in the same direction as the original motion

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Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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